The Universal Mobile Telecommunication System (UMTS) is one of the third generation mobile communication technologies designed to succeed the Global System for Mobile communication (GSM). 3GPP Long Term Evolution (LTE) is a project within the 3rd Generation Partnership Project (3GPP) to improve the UMTS standard to cope with future requirements in terms of improved services such as higher data rates, improved efficiency, and lowered costs. The Universal Terrestrial Radio Access Network (UTRAN) is the radio access network of a UMTS and Evolved UTRAN (E-UTRAN) is the radio access network of an LTE system. In an E-UTRAN, a user equipment (UE) 150 is wirelessly connected to a radio base station (RBS) 110a commonly referred to as an eNodeB (eNB), as illustrated in FIG. 1. The eNBs 110a-c are directly connected to the core network (CN) 190.
In a wireless communication system using Orthogonal Frequency Division Multiplexing (OFDM) technology, the entire channel is divided into many narrow sub-channels, which are transmitted in parallel. This technique thus transforms a frequency selective wide-band channel into a group of non-selective narrowband channels, making it robust against large delay spread by preserving the orthogonality in the frequency domain. The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe channel conditions without complex equalization filters in the receiver. Channel equalization is simplified because OFDM may be viewed as using many slowly-modulated narrowband signals rather than one rapidly-modulated wideband signal. The low symbol rate makes the use of a guard interval between symbols affordable, making it possible to handle time-spreading and eliminate inter-symbol interference.
In an LTE system the OFDM technology is adopted as a mean to achieve high transmission capability and robustness to multi-path delay. Orthogonal Frequency Division Multiple Access (OFDMA) is used in the downlink, and Single-carrier Frequency Division Multiple Access (SC-FDMA) is used in the uplink. OFDMA is a multi-user version of OFDM, where multiple access is achieved by assigning subsets of sub-carriers to individual users. SC-FDMA is a linearly pre-coded OFDM scheme. The distinguishing feature of SC-FDMA is that it leads to a single-carrier transmit signal, in contrast to OFDMA which is a multi-carrier transmission scheme. Furthermore, SC-FDMA has a lower peak-to-average power ratio which entails improved transmitter power efficiency for the battery-operated UE.
In LTE downlink, the physical layer is thus based on OFDMA. The transmitter structure for LTE downlink is illustrated in FIG. 2b. The information to be transmitted is coded e.g. by a turbo coding, interleaved, scrambled, and modulated to symbols. Some examples of modulation schemes are the Phase Shift Keying (PSK) modulations such as Quaternary or Quadrature PSK (QPSK), and the combinations of PSK and Amplitude Shift Keying (ASK) modulations such as 16 Quadrature Amplitude Modulation (QAM) and 64QAM. The symbols are fed to an Inverse Fast Fourier Transform (IFFT), where these symbols are mapped to a specified frequency interval specified as a number of sub-carriers. A resource block consists of 12 sub-carriers and is the smallest amount that a UE can be allocated. The IFFT is used to transform the symbols to be transmitted from a frequency domain representation to a time domain representation.
In LTE uplink, the physical layer is based on SC-FDMA, which is also referred to as pre-coded OFDM. This means that the physical channels are built of SC-FDMA symbols. The transmitter structure for LTE uplink is illustrated in FIG. 2c. The modulated symbols are transformed to the frequency domain by a Discrete Fourier Transform (DFT) of the same size as the number of modulated symbols of each SC-FDMA symbol. This is then fed to a larger IFFT with a size which depends on the bandwidth of the radio communication link.
In both downlink and uplink, a Cyclic Prefix (CP) is inserted at the output of the transmitter IFFT. The CP insertion implies that the last samples of the IFFT output block is copied and inserted at the beginning of the block. At the receiver side, the corresponding CP samples are discarded before demodulation by means of DFT processing, which means that support for calculating e.g. Fast Fourier Transforms (FFTs) is needed. An FFT is an efficient algorithm to compute the DFT and correspondingly the IFFT is used to compute the Inverse DFT (IDFT).
A radio communication between a UE and an RBS will be affected by multi-path propagation, fading, frequency errors, round trip times etc. This communication channel is often referred to as an air interface, and causes bit and block errors on information transmitted. A receiver is designed in order to reduce bit error and block error rates, and comprises e.g. FFTs, an equalizer and an antenna combining unit, as illustrated in FIG. 4. Another essential part of this receiver structure is the channel estimator.
Channel estimation has been widely used to improve the performance of OFDM systems. An accurate channel estimate is crucial for the equalization and thus also for demodulation and decoding of the user data. Pilot based channel estimation schemes are commonly used. In such a scheme known reference symbols—also called pilot symbols—are inserted at regular intervals in the time-frequency grid. Using the knowledge of the pilot symbols, the receiver can estimate the frequency domain channel around the location of the pilot symbol. As illustrated in FIG. 2a, the reference signals 230 are transmitted on the first, fifth, eight and twelfth symbol and occupy each sixth sub-carrier for LTE downlink and single stream transmission, while user data 220 is transmitted on the other sub-carriers. Each symbol is preceded by a CP 210 as described above. When multiple streams are utilized such as for Multiple Input Multiple Output (MIMO), more symbols are allocated to reference signals.
In FIG. 2d, the sub-frame format for LTE uplink is illustrated in which twelve symbols are allocated to user data 220, and two symbols are allocated to demodulation reference signals 230, for each sub-frame of one millisecond. Each symbol is preceded by a CP 210 as described above. The reference signals have the same resolution in frequency domain as the user data, as the same number of sub-carriers is allocated for reference signal symbols 230 as for user data symbols 220.
In a system where Multi-User MIMO (MU-MIMO) is used, several UEs may be scheduled to transmit simultaneously during the same time and frequency intervals, as illustrated in FIG. 3. These UEs can be distinguished by allocating different, and preferably orthogonal, reference signals to the different UEs, such that all channels from all transmit antennas to all receive antennas can be estimated. In MU-MIMO for LTE, the reference signals of the different UEs are based on different cyclic shifts of one basic reference signal.
The channel's frequency response across the whole bandwidth can thus be determined by interpolation using various channel estimation schemes. Several channel estimation algorithms are proposed based on DFTs or Discrete Cosine Transforms (DCTs). With DFT and DCT based channel estimation, the frequency domain channel estimate is transformed into a time or transform domain channel estimate and the time or transform domain properties of the channel are used instead of the frequency domain properties when estimating the channel.
An example of a known channel estimation algorithm based on DFT is described with reference to FIG. 4. In a first step, a matched filter channel estimate is calculated. The matched filter channel estimate ĤMF(k) may be determined as:ĤMF(k)=X*(k)Y(k)  (1)where k is the sub-carrier index, Y(k) is a received reference signal in the frequency domain and X*(k) is a complex conjugate of known demodulation reference signals. In a second step, this matched filter channel estimate is converted to the time domain by an IDFT. A time domain representation of this matched filter channel estimate ĥMF(m) is determined as:
                                                        h              ^                        MF                    ⁡                      (            m            )                          =                              1                                          N                c                                              ⁢                                    ∑                              k                =                0                                                              N                  c                                -                1                                      ⁢                                                  ⁢                                          ⅇ                                  j                  ⁢                                                            2                      ⁢                                                                                          ⁢                      π                      ⁢                                                                                          ⁢                      km                                                              N                      c                                                                                  ⁢                                                                    H                    ^                                    MF                                ⁡                                  (                  k                  )                                                                                        (        2        )            where m is a channel tap index, k is the sub-carrier index, and Nc is the number of sub-carriers for which reference signals are available. The fundamental period of the IDFT is equal to the number of sub-carriers for which the channel estimate is calculated, and is thus equal to the number of sub-carriers Nc for which reference signals are available.
In a third step, a window is applied to the matched filter time domain channel estimate ĥMF(m) which can be described as keeping the channel taps from a left channel tap index m=mL to a right channel tap index m=mR. The purpose of the windowing is to reduce the noise, by extracting only the relevant part of the channel in the time domain. Finally, in a fourth step, this windowed channel estimate is converted to the frequency domain with a DFT. The frequency domain channel estimate ĤDFT(k) is then determined as:
                                                        H              ^                        DFT                    ⁡                      (            k            )                          =                              1                                          N                c                                              ⁢                                    ∑                              m                =                                  m                  L                                                            m                R                                      ⁢                                                  ⁢                                          ⅇ                                                      -                    j                                    ⁢                                                            2                      ⁢                                                                                          ⁢                      π                      ⁢                                                                                          ⁢                      km                                                              N                      c                                                                                  ⁢                                                                    h                    ^                                    MF                                ⁡                                  (                  m                  )                                                                                        (        3        )            
For LTE downlink, the reference signals occupy only each sixth sub-carrier as illustrated in FIG. 2a, and the reference signal resolution is thus low. If the channel estimate in the frequency domain is required with a higher resolution than the available one, a zero padding of the time domain channel estimate may be done before performing the DFT. By zero-padding the time domain channel estimate to a length of six times the number of sub-carriers used for reference signals Nc, and then convert this extended time domain channel estimate to the frequency domain by a DFT, a channel estimate is achieved with the same frequency resolution as the user data symbols. For LTE uplink, the reference signals have the same resolution in the frequency domain as the user data, such that no time domain zero-padding corresponding to a frequency domain interpolation is needed.
It is also possible to include a zero-padding such that both the IDFT and the DFT are based on a higher fundamental period than the actual number of sub-carriers, in order to reduce the distortion in the band edges. Such a zero-padding is referred to as an over-sampling of the channel with an over-sampling factor KOS. In the example illustrated in FIG. 5, a channel of 48 sub-carriers is zero-padded up to double length, i.e. the over-sampling factor KOS is equal to two. A time domain channel estimate based on an over-sampled IDFT ĥosMF(m) is determined as:
                                                        h              ^                        osMF                    ⁡                      (            m            )                          =                              1                                                            N                  c                                ⁢                                  K                  os                                                              ⁢                                    ∑                              k                =                0                                                              N                  c                                -                1                                      ⁢                                                  ⁢                                          ⅇ                                  j                  ⁢                                                            2                      ⁢                                                                                          ⁢                      π                      ⁢                                                                                          ⁢                      km                                                                                      N                        c                                            ⁢                                              K                        os                                                                                                        ⁢                                                                    H                    ^                                    MF                                ⁡                                  (                  k                  )                                                                                        (        4        )            
With a rectangular window applied to this over-sampled time domain channel estimate, a windowed frequency domain channel estimate ĤosDFT(k) is determined as:
                                                        H              ^                        osDFT                    ⁡                      (            k            )                          =                              1                                                            N                  c                                ⁢                                  K                  os                                                              ⁢                                    ∑                              m                =                                  m                  L                                                            m                R                                      ⁢                                                  ⁢                                          ⅇ                                                      -                    j                                    ⁢                                                            2                      ⁢                                                                                          ⁢                      π                      ⁢                                                                                          ⁢                      km                                                                                      N                        c                                            ⁢                                              K                        os                                                                                                        ⁢                                                                    h                    ^                                    osMF                                ⁡                                  (                  m                  )                                                                                        (        5        )            
The applied rectangular window may be adaptive in the sense that both the left index mL and the right index mR are adjusted with a so called Akaike approach, in order to adaptively cover all main channel taps within the window. FIG. 5 illustrates the window applied in the frequency domain, which is thus a frequency domain interpretation of the rectangular time domain window.
In a DCT based channel estimation, the IDFT in the second step of FIG. 4 is replaced by a DCT, and the transform domain representation of the matched filter channel estimate ĥDCT(m) is given by:
                                                        h              ^                        DCT                    ⁡                      (            m            )                          =                              w            m                    ⁢                                    ∑                              k                =                0                                                              N                  c                                -                1                                      ⁢                                                  ⁢                                                                                H                    ^                                    MF                                ⁡                                  (                  k                  )                                            ⁢                              cos                ⁡                                  (                                                                                    π                        ⁡                                                  (                                                                                    2                              ⁢                                                                                                                          ⁢                              k                                                        +                            1                                                    )                                                                    ⁢                      m                                                              2                      ⁢                                                                                          ⁢                                              N                        c                                                                              )                                                                                        (        6        )            where w0=√{square root over (1/Nc)} and wm=√{square root over (2/Nc)} for 1≦m≦Nc−1. Moreover, the DFT in the fourth step of FIG. 4 is replaced by an IDCT.
A DCT may be described as a mirror extension of the spectrum to double length followed by an IDFT, as illustrated in FIGS. 6a-b. This means that a DCT can be calculated by a data manipulation—i.e. the mirror extension—followed by an IDFT, where the IDFT has a fundamental period equal to twice the number of sub-carriers. FIG. 6a illustrates the magnitude response for the DCT, and FIG. 6b illustrates the phase response for the DCT.
When applying a window to a transform domain channel estimate, a bias of the channel estimate occurs especially in the frequency edges, thus resulting in an inaccurate channel estimation which may negatively affect e.g. the equalization of user data in the receiver. This is true both when using an over-sampled DFT based channel estimation and a DCT based channel estimation.